Stability criteria for robot compliant maneuvers

A nonlinear approach for the stability analysis of robot manipulators in constrained maneuvers is presented. Stability of the environment and the manipulator taken as a whole has been investigated, and a bound for stable manipulation has been derived. The authors show that for stability of the robot, there must be some initial compliancy either in the robot or in the environment. The general stability condition has been extended to the particular case where the environment is very rigid in comparison with the robot stiffness. The stability analysis has been investigated using unstructured models for the dynamic behaviour of the robot manipulator and the environment. This unified approach of modeling robot dynamics is expressed in terms of sensitivity functions as opposed to the Lagrangian behavior of all the elements of a robot manipulator (i.e., actuators, sensors, and the structural compliance of the links) in addition to the rigid body dynamics